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gravity02

7.1.4 Example (N84/P2/Q7) Binary Stars

Example (N84/P2/Q7) Binary Stars

Two stars of equal mass M move with constant speed v in a circular orbit of radius R about their common centre of mass O. What is the net force on each star?

A   G M 2 R 2          B     G M 2 4 R 2           C    zero          D   2 M v 2 R 2           E    M v 2 2 R

7.1.4.1 Activity:

select from the down-drop menu "M1=M2=1,circular_orbit"

click play and observe the motion, noting down the magnitude of the forces (green arrows) on each mass.

let assume in the simulation that  M 1 = 1 s . m . = 1.988 x 1 0 30 k g    and M 2 = s . m . = 1.988 x 1 0 30 k g

given that astronomical unit is 1 a.u. = 1.496x1011 m

the distance between the masses is   R 1 + R 2 = 2 a .u. = ( 2 ) ( 1.496 x 1 0 11 ) m

the force is therefore, F 1 = G M 1 M 2 ( R 1 + R 2 ) 2 = ( 6.67 x 1 0 -11 ) ( 1.988 x 1 0 30 ) ( 1.988 x 1 0 30 ) ( ( 2 ) ( 1.496 x 1 0 11 ) ) 2 = 2.94 x 1 0 27 N


therefore net force on each M1 star is F 1 = G M 2 4 R 2

similarly, the net force on M2 star is F 2 = G M 2 4 R 2 making the answer B

in  the simulation terms, notice the force on M1,  F1 = (2.98x1026)9.81 N and F2 = (2.98x1026)9.81 N.


Model: You may view the movement of the two stars using the EJSS below link (require internet) or just below:

7.1.4.2 Model: 

You may interact with the simulations using the EJSS below link (require internet) or just below if you are using the epub3 reader such as Gitden Reader(Android) or iBook(Apple). It is recommended to enable Scrolling View equal to true by clicking on the AA on the top right corner of the reader app, so as to maximize the view of the simulations.
  1. Run Sim
  2. http://iwant2study.org/ospsg/index.php/272
 

For Teachers

Translations

Software Requirements

SoftwareRequirements


Android iOS Windows MacOS
with best with Chrome Chrome Chrome Chrome
support full-screen? Yes. Chrome/Opera No. Firefox/ Samsung Internet Not yet Yes Yes
cannot work on some mobile browser that don't understand JavaScript such as.....
cannot work on Internet Explorer 9 and below

 

Credits

Fu-Kwun Hwang - Dept. of Physics,National Taiwan normal Univ.; Loo Kang Wee; Wolfgang Christian

end faq

http://iwant2study.org/lookangejss/02_newtonianmechanics_7gravity/ejss_model_gravity02/gravity02_Simulation.xhtml

 App

 Cover arthttps://play.google.com/store/apps/details?id=com.ionicframework.gravity02app385564&hl=en

YouTube

Versions

  1. http://weelookang.blogspot.sg/2016/07/binary-stars-javascript-model-by-fu.html

Other resources

  1. https://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html

 

 

end faq

 

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